Question

(a) Evaluate the integral $int_C frac{dz}{1 + z^2}$ where C is the circle with centre -2i and radius 2 traversed anti-clockwise. (b) Let a be a fixed complex number different from zero. Let $C_R$ denote the circle with centre at 0 and radius $R eq |a|$ traversed anti-clockwise. What are the possible values of the integral $int_{C_R} frac{sin z}{(z - a)^3} dz$? Justify your answer.

          (a) Evaluate the integral
$int_C frac{dz}{1 + z^2}$
where C is the circle with centre -2i and radius 2 traversed anti-clockwise.
(b) Let a be a fixed complex number different from zero. Let $C_R$ denote the circle with centre at 0 and radius $R 
eq |a|$ traversed anti-clockwise. What are the possible values of the integral
$int_{C_R} frac{sin z}{(z - a)^3} dz$?
Justify your answer.

$(a) Evaluate the integral intC fracdz1 + z^2 where C is the circle with centre -2i and radius 2 traversed anti-clockwise. (b) Let a be a fixed complex number different from zero. Let CR denote the circle with centre at 0 and radius R eq |a| traversed anti-clockwise. What are the possible values of the integral intCR fracsin z(z - a)^3 dz? Justify your answer.$

Added by Aaron T.

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